A Sensitivity Approach to Assessing Model Uncertainty for Stochastic Systems

该奖项的研究目标是开发一种稳健和易处理的方法来评估输入模型误差的影响，并对输入模型的参数形式进行最小限度的假设。在许多随机估计问题中，模型假设与实际之间的偏差或输入模型误差是一个重要的问题，因为它会在不同程度上影响输出的精度。其关键部分是关于非参数统计距离的一类灵敏度估计，它是通过对概率空间上的最优化问题的新的无穷小分析而得到的。这些灵敏度估计器是稳健的，因为它们自动捕捉模型空间中沿最坏情况方向的模型差异，并且它们通过高效的蒙特卡罗方法在计算上是容易处理的。在理论上，它们将有助于对随机计算中模型风险的基本了解，在实践方面，它们可以广泛用于对模型假设的可靠性进行压力测试。如果成功，本研究结果将为评估在许多应用中出现的计算中的模型风险的影响提供一种稳健且可实现的方法。制造业、通信、呼叫中心、金融风险管理等行业都需要定期进行不同绩效指标的测算。研究得出的方法将提供敏感性分析工具，以衡量这些计算中不准确的模型假设的影响和风险。这项研究的结果还将用于开发本科生和研究生水平的新课程，并建立对代表不足群体的学生的指导。这一实施将通过学术和工业用的开放软件广泛传播。

The research objective of this award is to develop a robust and tractable methodology for assessing the impact of input model error, with minimal assumption placed on the parametric form of the input model. The discrepancy between model assumption and reality, or input model error, constitutes an important concern in many stochastic estimation problems, since it can affect the accuracy of outputs in various magnitudes. The key ingredient is a class of sensitivity estimators that are taken with respect to nonparametric statistical distances, derived via a new line of infinitesimal analysis on optimization problems over probability space. These sensitivity estimators are robust in that they automatically capture model discrepancy along the worst-case directions in the model space, and they are computationally tractable via efficient Monte Carlo methods. On the theoretical side, they will help provide fundamental understanding of model risk in stochastic computation, and on the practical side, they can be widely used to perform stress tests on the reliability of model assumptions.If successful, the results of this research will provide a robust and implementable method to assess the effect of model risk in computations that arise in many applications. Industries such as manufacturing, communication, call centers, and financial risk management all need to carry out calculations of different performance measures on a regular basis. The methodologies that come out from the research will provide sensitivity analysis tools to measure the impact and risk of inaccurate model assumptions in these calculations. The results of this research will also be used to develop new courses in undergraduate and graduate levels, and to establish mentorship of students from under-represented groups. The implementation will be widely disseminated through open software for both academic and industrial use.